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Having a bit o' fun with math.


Mar
17
comment Using Black-Scholes Equation to “buy” stocks
Yes, and if you want to take into account the risk of bankruptcy, you can model the company as a barrier option...
Mar
17
comment Using Black-Scholes Equation to “buy” stocks
Short answer is that Black-Scholes is not likely to help you. You may want to look into models of company fundamentals. B-S is a model for pricing derivative instruments (assuming features of the stock, get value of options). [Note that nothing I say should be construed as giving financial advice. I am not a financial advisor.]
Mar
17
answered Using Black-Scholes Equation to “buy” stocks
Mar
17
comment [Model Theory] Problem
No complaints with that one.
Mar
17
comment [Model Theory] Problem
Elementary equivalence is not the same thing as isomorphism, so this is not sufficient. (Two structures need not even be the same cardinality to be elementarily equivalent.) It is not clear that the assertion that a monoid is generated by a single element is expressible in a first-order sentence in the language with $0$ and $+$.
Mar
17
answered Topology exercises
Mar
10
comment What does a hat or star means in math?
Absolutely! I guess the point is that there is no "standard" usage across all of mathematics, though there are "local" conventions. (Set theorists will have different conventions than K-theorists...)
Mar
10
answered What does a hat or star means in math?
Mar
8
comment If a basis of a topology has order no greater than the weight, is it contained in all other bases?
I would assume it is the weight of the space, the minimum cardinality of a basis.
Mar
3
awarded  Critic
Mar
2
comment How to compute the series $\sum_{n=0}^\infty q^{n^2}$?
The series itself is obviously very quickly converging and using a partial sum gives a good estimate. You can use the identity $\theta(-1/\tau) = (-i\tau)^{1/2}\theta(\tau)$ where $\theta(\tau) = \sum_{n=-\infty}^\infty q^{n^2}$ with $q=e^{\pi i \tau}$ to move $q$ near $1$ to near $0$ to get faster convergence for those more slowly convergent points.
Mar
2
answered Is it possible to prove that the metric space is an open set without choice?
Feb
14
comment What is an efficient algorithm to compute modular exponentiation of stacked exponents?
This is Fermat's little theorem: if $\gcd(b,m)=1$ then $b^{m-1}\equiv 1 \pmod{m}$.
Feb
12
awarded  Commentator
Feb
12
comment Cardinality of all lines on $\mathbb R^{2}$ which do not contain point $(x,y)\in l$ where $x, y \in \mathbb Q$
Yep, though Ma.H did mention that the upper bound was obvious, so I didn't elaborate. (Though never hurts to give the complete argument).
Feb
12
comment Cardinal arithmetic
It's the only answer, so as bad as it is... :-) (Maybe if I remove the dependence on AC I'll get a vote?)
Feb
11
revised Cardinal arithmetic
added 814 characters in body
Feb
11
answered Cardinal arithmetic
Feb
11
revised Cardinal arithmetic
Texified and corrected problem with $x=1$.
Feb
11
suggested suggested edit on Cardinal arithmetic